same, agree, equal
同 centers on sameness: things that are identical, equal, or in agreement. It expresses the idea of matching or being the same as something else.
same; identical; equal; alike; equivalent
the same; the said
same; similar; (just) like; equal
at the same time; at once; simultaneously; concurrently
fellow; mutual; companion; comrade
cooperation; collaboration; association; partnership; (acting in) unison
agreement; consent; approval; assent
coworker; co-worker; colleague; associate
in the same way; like; likewise; similarly
same person
same time
alliance; union; league
the same company; the said firm
same period; corresponding period
classmate
accompanying (someone); going with; travelling together
combination; union; joining; incorporation; amalgamation; merger; fusion
sympathy; compassion; pity
equality; equal; same rights; same rank; equivalence
identical; same; one and the same; equal
living together; coexistence
homosexuality; homosexual love
like-mindedness; (being of the) same mind; shared sentiment
the same day
同 is thought to depict a container or cover with an opening, later used to express the idea of sameness or gathering together. The exact historical development is uncertain.
The shape 同 looks like a uniform box with a single opening, suggesting everything inside is the same. Picture a container where all items are identical.
For ドウ, imagine a doughnut box where every doughnut is exactly the same: dough -> ドウ, and they all agree in shape and flavor.